A lawyer advising National Security Agency leaker Edward Snowden has said his asylum status has not been resolved and that he is going to stay at the Moscow airport for now.

Anatoly Kucherena, who was visiting Snowden at Moscow's Sheremetyevo airport on Wednesday, said that migration officials are still looking at his asylum request and the process had been drawn out.

Kucherena said that Snowden is staying in the transit zone "for now" and "intends to stay in Russia, study Russian culture."

Law enforcement and airport sources had earlier said Snowden had been issued documents confirming his asylum request was being considered and would be allowed to leave the airport transit zone.

Kucherena told state news agency RT on Tuesday Snowden was "planning to arrange his life here. He plans to get a job. And I think that all his further decisions will be made considering the situation he found himself in."

The US has been seeking Snowden's extradition to face felony charges for leaking details of US surveillance programs. Russia has refused to hand him over, while denying that it had anything to do with his travel plans.

Snowden was stranded in the Moscow airport transit zone, which is technically not Russian territory, on 23 June, after US authorities annulled his passport while he was travelling from Hong Kong. Presidents Barack Obama and Vladimir Putin reportedly discussed the issue during a phone call in mid-July.

In a meeting with government and human rights officials on 12 July, Snowden announced he would seek temporary asylum in Russia while hoping to eventually travel on to South America, where Bolivia, Nicaragua and Venezuela have said they would offer him asylum. The US has prevented him from flying there, Snowden said, apparently referring to the possibility that any flight carrying him would be forced to land by the US or its allies.

Experts had expressed doubts that Snowden would be allowed to leave the airport.

Former immigration service head Vladimir Volokh said it was likely he would not be allowed to move freely about the country, and that further procedures related to his asylum request would take place in the transit zone or a temporary holding centre, he told radio station Kommersant FM.

"Legally he won't be forbidden [to move about], but the main question here is guaranteeing his safety," Volokh said.

Kucherena is a member of the Public Council of the Federal Security Service, the successor to the KGB, which lends fuel to speculations that Snowden's stay is being handled by Russia's intelligence services.